## College Algebra (10th Edition)

$x=2.53$
We test $f(x)=x^{3}+x^{2}+x-4$ on nonnegative integer values of x, and find that $f(2)$is negative, $f(3)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2,3].$ Subdividing $[2,3]$ into 10 subintervals, calculating f( endpoints), we find $f(2.5)$is negative, $f(2.6)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.5,2.6].$ Subdividing again, we find $f(2.53)$is negative, $f(2.54)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.53,2.54].$ The real zero is $x=2.53...$ To two decimal places, $x=2.53$